Looks like (from a quick googling, may be something I'm not taking into account here) violent crime is actually more common in Australia than in California.
Australia 692 violent assaults per 100k [1]
California 430 assaults per 100k [2]
So, you'd also be trading more of a rare really bad thing for less of a relatively common bad thing.
An obvious flaw is that it's comparing an entire country to a singular (and disporoprotionately wealthy) state. If you expanded the rate to America in general the violent crime rate is around 800 per 100k, and if you reduced "Australia" to "New South Wales" then you also see a similar drop - but the site doesn't provide an easy to consume summary.
> An obvious flaw is that it's comparing an entire country to a singular state.
California has a much larger population and twice the economic output of Australia. It seems much more reasonable to compare Australia to one state than to compare it to the entire US.
Why would you compare it to the US? The US has an order of magnitude more people. California is comparable in population. The right thing to do would be to compare the locales where you would spend time in each place, e.g. the violent crime rate in your neighborhood or would-be neighborhood matters most, then city, and maybe state.
That assumes assaults in the US are reported the same way. Murders probably are because there is a body. I doubt I her crime is given the weird incentives in the US system.
The web app doesn't seem to support direct linking to query results, but it's in here: http://crimetool.bocsar.nsw.gov.au/bocsar/ under Assault - Non Domestic.
At the end of the day though - people tend to consider being murdered a significantly more disruptive event than getting punched in the face.